The Scot was relieved of his duties at Old Trafford just 10 months into a six-year contract, and his Blues counterpart has expressed his sympathies
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Louis van Gaal is the favourite to take over the vacancy, despite links with Tottenham, and is known to be "very keen" on the role, although first-choice candidate Jurgen Klopp has distanced himself from an approach.
Real Madrid manager Carlo Ancelotti previously admitted his surprise at the sacking and Mourinho - who was linked with the Old Trafford job before Moyes was appointed - has echoed the Italian's sentiments.
"I prefer not to comment. I feel sorry for him, obviously," he told ITV.
"I just feel sorry for David like I feel sorry for every manager who loses his job."
Moyes, who created a host of unwanted records during his brief stint at Old Trafford, has become the first United manager to be dismissed since Ron Atkinson in 1986.